Semenyo played the entire match as Palmer was substituted in the second half.
At a Glance
Two assists from Semenyo's long throw-ins led to strikes by Brooks and Kluivert.
Chelsea's goals came from Palmer and Fernandez during a chaotic opening 45 minutes.
Enzo Fernandez missed the best opportunity of a goalless second period.
Bournemouth forward Antoine Semenyo, reportedly close to a big-money transfer, was at the heart of the action, providing two assists and conceding a penalty in a dramatic 2-2 stalemate against Chelsea.
Despite being on the verge of a lucrative switch, the 25-year-old attacker started for his club. He utilized his long throw expertise to great effect, creating scoring opportunities that were finished by Brooks and Kluivert.
Brooks opened the scoring just six minutes in, converting from close quarters after a dangerous long throw from Semenyo.
Chelsea responded and then took the lead after Semenyo fouled Estevao Willian inside the penalty area. The match official awarded a penalty after a review by the Video Assistant Referee system.
Palmer calmly dispatched the penalty, placing it perfectly into the corner even though the keeper dove the right way. Fernandez made it 2-1 with a stunning strike into the top corner midway through the first half.
Kluivert leveled the scores again shortly after, tapping home from another precise long throw delivered by Semenyo.
The visitors finished the first period on top, forcing Sanchez into several saves from their 14 first-half efforts.
At halftime, Chelsea's manager made two changes, introducing captain Reece James and Pedro Neto for Josh Acheampong and Alejandro Garnacho.
Early in the second half, a handball appeal against Malo Gusto was dismissed by the VAR official. Former Chelsea goalkeeper Djordje Petrovic then produced an excellent save to deny Estevao from distance.
The best chance of the second half fell to Enzo Fernandez in the 77th minute, but he blazed his shot over the bar from inside the box.
Palmer's withdrawal for Pedro was greeted by boos from a section of the home crowd as the manager's side sought control. Despite growing dominance in the latter stages, Chelsea could not find a decisive late goal.
In injury time, Bournemouth substitute Enes Unal volleyed over from 12 yards out after a cross from Amine Adli.
This draw extends Chelsea's poor run to only one win in their previous seven Premier League matches. For Bournemouth, the point does little to improve their own form, as they remain without a win in ten games.
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